Constructing local integrals of motion in the many-body localized phase

ORAL

Abstract

We consider a many-body localized spin system and its description by the so-called l-bit Hamiltonian. We outline a renormalization flow procedure to construct the extensive set of conserved quantities, and demonstrate that their locality results in exponentially decaying interactions in this effective model. The associated localization length of this decay is shown to manifest properties very similar to the noninteracting case of Anderson localization: normality of its distribution across samples, and its direct qualitative correspondence to the local spectral properties. A numerical simulation of a magnetic spin-echo protocol quantitatively reproduces these theoretically computed length scales. We therefore argue that these local integrals of motion help to practically identify the many-body localized phase.

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Presenters

  • Vipin Kerala varma

    College of Staten Island

Authors

  • Vipin Kerala varma

    College of Staten Island

  • Vadim Oganesyan

    Physics and Astronomy, CSI and GC, CUNY, College of Staten Island

  • David Pekker

    University of Pittsburgh, Department of Physics and Astronomy, University of Pittsburgh, Physics and Astronomy, University of Pittsburgh

  • Abhishek Raj

    College of Staten Island

  • Sarang Gopalakrishnan

    CUNY College of Staten Island, and CUNY Graduate Center, Physics, CUNY College of Staten Island, Physics and Astronomy, CSI and GC, CUNY, CUNY College of Staten Island; The Graduate Center, CUNY, Department of Physics and Astronomy, CUNY College of Staten Island, Physics, CUNY, College of Staten Island, City University of New York, Physics, The Graduate Center, CUNY